There was nothing inevitable about it, nor is there anything conventional about him. Born in Canada, elected to the Senate from Alberta’s muscular cousin, Texas, Mr. Cruz has until this month been overshadowed by his slightly younger fellow Cuban-American, Sen. Marco Rubio of Florida. No more. Mr. Cruz has soared to the lead in almost every poll in Iowa, eclipsing even Donald J. Trump, and ranks second to the billionaire businessman in almost every national poll.

If there is an alternative to Mr. Trump right now — and remember, as a cautionary note, how Republican polls and primary results swung like bungees only four years ago — it is Mr. Cruz. That itself is not only astonishing but also significant.

Astonishing: Because only last month, Mr. Cruz, who turns 45 Tuesday, trailed Mr. Trump by margins well into double digits.

Significant: Because Mr. Cruz has deliberately and carefully courted Mr. Trump’s support base even as he was building his own. Though the two are temperamentally and rhetorically different, they draw on many of the same themes, and if you add their support together you get a remarkable congruence: 53 percent of Republican support in the Iowa caucuses and 53 percent of Republican support nationally. It may be the first time ever that the Iowa and national numbers have converged exactly.

More significance: This tells us that the well of alienation within the Republican Party is even deeper than earlier surveys suggested. The Duo of Discontent has tapped into — perhaps even, by virtue of their fiery rhetoric and distilled contempt for the GOP establishment, expanded — a growing rebellion in American politics.

And so while it is tempting to argue that Mr. Trump is an American original, tycoons, outsiders, agitators and media phenoms have been a big part of our political tradition. The real American original may be Mr. Cruz, particularly since his American story begins in the peaceable kingdom north of the 49th parallel with a mother holding a degree from Rice University and a father who got his education in the rebellion in Batista Cuba.

And while Mr. Trump may seem to have built a candidacy out of unlikely elements, including an Ivy League education, a real-estate empire and vast exposure on “The Apprentice,” Mr. Cruz’s profile is even more unlikely.

He is grumpy. There is none of the “lift of a driving dream” that Ray Price added to Richard Nixon’s rhetoric for his speech at the Highway Hotel in Concord, N.H., in his 1968 campaign — a speech that has become a symbol of the rhetoric of hope that even dyspeptic candidates employ in presidential elections. Nor are there the touches of Tennyson that Theodore Sorensen gave John F. Kennedy in 1960 and that Jeffrey Hart gave Ronald Reagan in 1976 and 1980. And no one describes Mr. Cruz as a Happy Warrior, the phrase from Wordsworth that Franklin Delano Roosevelt appropriated for Al Smith in 1928, that Hubert Humphrey ascribed to himself in 1968 and that Barack Obama applied to Joseph R. Biden Jr. in 2008.

But there is more. Mr. Cruz is no mellifluous speaker. His voice has the capacity to curdle milk in a refrigerator two blocks away and to scratch blackboards in a middle school at the far edge of town. He’s reviled by his colleagues, who consider him selfish, self-absorbed, self-indulgent and, when he began his presidential campaign, self-deluded. They were wrong about the latter. And while Mr. Cruz, a Supreme Court clerk to Chief Justice William H. Rehnquist, is almost always the smartest man in the room, he seldom is the nicest.

No matter. The great 1950s American political philosopher Leo Durocher taught us the perils of being a nice guy; after all, Mr. Nixon was on a national ticket five times and another unlikely insurgent, Jimmy Carter, who once was as low as Mr. Cruz was in national polls, is less likely to be enshrined in the congeniality hall of fame than Pete Rose is to win a place in the Baseball Hall of Fame.

Mr. Cruz, however, is blazingly smart, and blazingly fast on his feet. Sometimes speed kills — he hasn’t walked back his comment about taking the battle to the Islamic State and seeking to discover “if sand can glow in the dark” — but overall his quickness is a substantial asset.

Earlier this autumn, Mr. Cruz launched an attack against the CNBC debate moderators that could not have been rehearsed and could not have been more pitch-perfect. In Tuesday’s debate in Las Vegas he parried Mr. Rubio’s thrusts with ease if not exactly with elan. And his remark that President Barack Obama has practiced “photo-op foreign policy” displayed a mastery of alliteration for the alienated.

Mr. Cruz also scored points for employing the phrase “political correctness” — a rhetorical neutron bomb after campus protests at the University of Missouri and Yale — to characterize Mr. Obama’s approach to terrorism surveillance and to tie the president to some of Mr. Cruz’s Republican rivals. “[B]ecause of political correctness the Obama administration, like a lot of folks here, want to search everyone’s cellphones and emails and not focus on the bad guys,” Mr. Cruz said. “And political correctness is killing people.”

His fast talk and his fast rise are accompanied by a brawny campaign structure in Iowa, where speeches are consumed with avidity but where caucus votes are won by organizational activity.

The Cruz campaign might be described theatrically: The Force Awakens. It has campaign chairs in all 99 counties, supplemented by a cadre of pastors in three-quarters of them — and a dormitory arrangement for volunteers who, says Brian English, Mr. Cruz’s Iowa campaign director, will be coming to the state, some staying until the caucuses Feb. 1.

“We’ve got folks on the ground and people everywhere,” Mr. English says. “We’re working on training leaders in every precinct. We have a campaign that is as robust as any in this state, designed to get people to caucuses in a way unmatched by any other organization.”

Mr. Cruz no longer is cozying up to Mr. Trump and, with remarks questioning his rival’s judgment, is seeking to extend the distance separating them even as he pursues Mr. Trump’s supporters. In a Cruz television ad critical of Mr. Obama’s Islamic State policy, the narrator opens by saying, “There’s a scorpion in the desert.” Mr. Trump might be excused if he came to realize that there now is a scorpion in the prairies as well.

David Shribman, a Pulitzer Prize winner in journalism, is executive editor of the Pittsburgh Post-Gazette.